Fixed Income Quantitative Credit Research 7 August 2003

Up-front Credit Default Swaps
Dominic O’Kane and Saurav Sen
When bonds are distressed, protection is often quoted as an up-front payment rather than a “running” spread paid until the earlier of default or maturity. This article examines the pricing, risk profile and performance of up-front credit default swaps and compares them to the standard running trades.

This means that protection buyers make only a single up-front payment at initiation in return for protection against a credit event (typically these are bankruptcy. However. protection-sellers quote prices on an up-front basis. See O’Kane and McAdie (2001) for a discussion. Following this. vol. i.1. the net P&L of a trade. We also discuss default swap basis trades using up-front CDS and consider when up-front may be preferred to running. is strongly dependent on the timing of the credit event that triggers protection. This article examines the pricing. the protection buyer in an up-front CDS makes a single initial payment to the seller. While a default swap offers principal protection. funding and carry. We then examine the risk sensitivities of up-front CDS and compare these to running CDS. which incorporates coupons.
1
Reprinted from Quantitative Credit Research Quarterly. which has implications in terms of the interest rate risk. and applies to both running and up-front trades. Volume 2003-Q3.com When bonds are distressed. We call this a running CDS as the protection payments run throughout the life of the contract. 2003-Q3
Up-front Credit Default Swaps
Dominic O’Kane +44-20-7260-2628 dokane@lehman. Paying for protection up-front has the effect of changing the risk profile of the default swap contract in two fundamental ways. it front loads the timing of cashflows to the start of the trade. In particular. risk profile and performance of up-front credit default swaps and compares them to the standard running trades. in return for protection until a specified maturity date. which terminates following a credit event. when the reference credit is distressed. Unlike a standard CDS.com Saurav Sen +44-20-7260-2940 sasen@lehman.Lehman Brothers | Quantitative Credit Research
QCR Quarterly.
August 2003
Please see important analyst(s) certifications at the end of this report.1
1. We also address the issue of how an investor can decide whether to trade on an up-front or a running basis. funding costs and the cost of protection. First. Second.
1
. We begin by describing the precise mechanics of the up-front contract.
2. we set out the model for pricing up-front protection and discuss calibration issues. These contracts are also usually entered into for short maturities. protection is often quoted as an up-front payment rather than a “running” spread paid until the earlier of default or maturity. It should be noted that buying a bond and buying protection on the same face value is not a credit-neutral strategy when the bond is trading away from par.
INTRODUCTION
In the standard credit default swap (CDS). up to one year. UP-FRONT PROTECTION
2. where it costs nothing to enter into the contract.e. it removes the credit risk in the payment of the premium in the standard CDS. the protection buyer pays for protection by making regular spread payments to the protection seller until the earlier of a credit event or maturity of the contract. This effect is most pronounced when the issuer is distressed. The aim of this article is to set out in detail the mechanics and risks of the up-front CDS contract. failure to pay and restructuring) until the contract maturity date. Mechanics of Up-front Protection An up-front CDS is a contract that enables an investor to buy protection against the risk that an underlying reference entity suffers a credit event. we wish to highlight the differences between up-front and running CDS so that the investor can easily see which is more suitable for expressing a specific credit view.

exactly as in a standard running CDS. Pedersen and Turnbull.2. up-front protection is priced so that. The up-front price equals the arbitrage-free expected value of the risky coupon stream in a running CDS. Up-front versus Running Trades The difference between up-front and running CDS is in the premium leg: in the former case the cost of protection is delivered as a single amount paid at initiation. If default occurs before maturity. Figure 1 shows a schematic representation of the cashflows in running and up-front CDS contracts. the decision to trade on running or up-front basis also depends on the investor’s risk preferences. hence. as mentioned in the Introduction. to the protection seller in return for the face value amount in cash. the different timing of cashflows changes the distribution of outcomes. There are a number of reasons why dealers prefer to quote distressed credits in up-front format:
2 See “Valuation of Restructuring Credit Event in Credit Default Swaps”. The investor is then assuming the credit risk of the reference credit until the maturity date of the contract. As we explain below. Lehman Brothers Quantitative Credit Research Quarterly. the protection may be settled in cash format.
Figure 1: Comparison of cashflows for running and up-front default swaps. whereas in the latter it takes the form of a risky coupon stream which lasts until a credit event or maturity. Alternatively. May 2003. 2003-Q3
Equally. whichever occurs sooner. O’Kane.
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. Protection Seller Up-front Payment Running Spread
Time Running Up-front Protection Buyer 100-R on Credit Event
2. However. and also changes the risk profile of up-front trades relative to running. These concepts are illustrated with examples in the next section.Lehman Brothers | Quantitative Credit Research
QCR Quarterly. More details on the exact definitions of credit events and the mechanics of delivering protection can be found in O’Kane (2001). the protection buyer typically delivers assets with a face value equal to that of the protection. vol. an investor can use the up-front contract to sell protection in return for a single initial payment. The value of protection delivered is equivalent to par minus recovery. where recovery is the price of the cheapest-to-deliver (CTD) asset in the basket of deliverables2. This difference in the timing of cashflows enables investors to take a view on the timing of default. an investor should be indifferent between running and up-front trades. on a present value basis.

when protection is bought on an up-front basis. They can also be used to express views on the likely timing of default and expected spread movements. 2. We also assume that the funding rate and reinvestment rates are Libor flat at a constant 3%. This is also the regime in which bonds begin to trade on a price basis.
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. For simplicity. 2003-Q3
1. This is especially true when spreads are wide. It is no surprise that the same should happen to CDS.
An investor’s preference for up-front or running trades. For this reason.
4. UP-FRONT TRADES
As with running CDS. Suppose initially this bond was distressed. These examples illustrate the mechanics of up-front protection and also highlight the market views and risks implicit in such trades. To discuss these. we will assume that the bond and running CDS cashflow dates are synchronized. The distribution of outcomes from an up-front contract is typically narrower for an up-front CDS than for a running CDS.1. This will be explained in detail later. also depends on the valuation and price sensitivity of up-front trades. the payment of the accrued premium following a credit event has a significant effect and must be implemented correctly. the model-implied CDS spread corresponding to this up-front price. it is best to use an example and for this we will use a 5-year maturity. therefore. we describe some examples to fix ideas and motivate the remainder of the article. which is what would be required for many distressed credits. Before discussing these. is 1050bp. vol. 6% coupon bond which pays annually.
They eliminate any uncertainty about the size and timing of the payment for protection. Very wide spreads may also pose problems for analytics unless carefully implemented.
3. Dealers may feel more uncomfortable quoting spreads in excess of 1000bp. up-front CDS can be used to implement basis trades between the cash and CDS market. 3. assuming a 40% recovery rate. Cashflows to the investor are shown with a positive sign. trading at a clean price of $75 with an up-front premium quoted at $33 on a face value of $100.
3. risk aversion makes protection sellers and buyers prefer up-front to running. carry and MTM for a range of scenarios. The generic basis trade will consist of an investor being long the bond and long protection on the same face value via either a running or up-front CDS.Lehman Brothers | Quantitative Credit Research
QCR Quarterly. Scenario I: Reference Credit Survives to Maturity Table 1 shows the protection buyer’s cashflows in the event that the bond does not default. As we will show in the next section. We now examine the differences between running and up-front trades in terms of cashflows. For example.

76 5. In each period. exceed the $6 coupon income from the bond.00 0. but the total reinvested carry over the life of the trade is still positive.24 NET ($) 0.75 -6.76 -5. This is a negative carry trade.50 Funding ($) 75. Even though the last cashflow is positive to the investor.00 -6. in order to avoid locking in a high contractual spread for the life of the trade.76 2.
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.50 -10.24 -111.55 6.00 -10.00 106.24 -3.53 11.00 2.76 2. and the 3% funding paid on a total initial borrowing of $108 ($75 for the bond + $33 up-front protection).00 -3.76 2.76 per $100 face. which is the difference between the 6% coupon earned on the bond.60 8.50 running protection and $2.50 -10.70 -20. 2003-Q3
Table 1: Long Bond + Long Up-front Protection (No-default Scenario)
Time (Y) 0 1 2 3 4 5 Bond ($) -75.86 -28. Scenario II: Reference Credit Defaults After One Year Table 3 shows the cashflows for a protection buyer in a basis trade if a credit event occurs one year after the trade date.24 -3. We have assumed that the credit event happens just after the first coupon date.00 6. the net carry is $2.
Table 2: Long Bond + Long Running Protection (No-default Scenario)
Time (Y) 0 1 2 3 4 5 Bond ($) -75.00 6.50 -10. 3.00 6.25 -2.24 Reinvested carry ($) 0. Contrast this with Table 2 below.25 -2. as the investor has to pay back the funding principal.25 bond funding.00 Funding ($) 108.00 Upfront CDS ($) -33.00 -2. The last payment is negative. The protection has been purchased in up-front format.75 -6.Lehman Brothers | Quantitative Credit Research
QCR Quarterly.75 -13. consisting of $10.00 Running CDS ($) 0.00 0. would prefer to pay for protection in up-front form rather than a running spread. a protection buyer who expects the reference credit to survive but wishes to hedge his downside “just in case”.65
As Table 1 shows.00 -6.25 -77.00 6. the net reinvested carry is still negative.24 -3.00 6. buying up-front protection results in a positive carry trade.00 2.2.84
In this scenario.25 -2.24 -10.00 6.00 0. since the total payments in each period.75 -6.00 106.00 0.75 18.00 6. and the issuer defaults with 35% recovery. vol.50 -10.00 0.25 NET ($) 0.00 6.25 Reinvested carry ($) 0. which shows the cashflows when protection is bought on a running basis.

Compare this with the case of running protection.00 -108.
Time (Y) 0 0.24
Following the credit event.00 Reinvested carry ($) 0. Table 5 shows the unwind value of the trade three months after the trade date.81 -0.25.50 Funding ($) 108.
Table 5.00 2.00 Funding ($) 108. which corresponds to an up-front price of $18.00 92.75 25.24.25 -75. 3.00 Reinvested carry ($) 0. protection buyers who have a view that default is almost certain should prefer to trade on a running CDS format.25
The protection payout following the credit event is the same as in the up-front case.00 -10.81 MTM ($) 1.Lehman Brothers | Quantitative Credit Research
QCR Quarterly. The protection buyer does better in the running CDS format.00 6.00 -2.69
We see that the gain in the value of the bond has been almost exactly offset by the fall in the value of the up-front CDS and the funding. Protection sellers who view default as imminent should prefer to trade on an up-front basis.00 NET ($) 0. To illustrate this.75 18.00 NET ($) 0.00 6. Scenario III: Bond Rallies Sharply In Three Months Consider now a scenario where the bond price rallies from $75 to $92 in three months.50. but has to repay the funding principal of $108. 2003-Q3
Table 3: Long Bond + Long Up-front Protection (Default Scenario)
Time (Y) 0 1 DEFAULT Bond ($) -75.25 UNWIND
Unwind Value of Up-front Trade (Bullish Scenario)
Bond ($) -75. The presence of a risky premium leg makes the unwind value of a running CDS more sensitive to spread movements than an
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. The reinvested carry from the trade is therefore a negative -$5.00 Upfront CDS ($) -33. This is illustrated in Table 4 below in the same scenario as above.00 -6.00 65. the protection buyer receives $35 from the sale of the distressed bond and $65 from the up-front CDS.24 -108. if protection is purchased on an up-front basis. The net reinvested carry from the trade is therefore $18.00 Running CDS ($) 0.00 Funding ($) 75. Suppose the quoted running spread for the issuer now stands at 495bp.
Table 4: Long Bond + Long Running Protection (Default Scenario)
Time (Y) 0 1 DEFAULT Bond ($) -75.00 2. which nets a positive cashflow of +$25 to the protection buyer.00 -3.00 18.3. but the funding principal to be repaid is $75.50 -14. vol. As a result.76 -5.00 0.00 35. Compare this to a protection buyer who chooses to trade on a running basis.76 -8.00 35.00 Upfront CDS ($) -33.00 -6.50 65.00 17. resulting in a net negative cashflow of $8.

24 3.56 MTM ($) -3. vol.84 18. 3.25 UNWIND
Unwind Value of a Running Trade (Bullish Scenario)
Bond ($) -75.
Scenario Issuer survives to maturity Credit event in 1 year Credit event in 4 years Spreads tighten Spreads widen
P&L of Trades: Upfront versus Running (Various Scenarios)
Running ($) -10.84 Upfront ($) 6. we see that the absolute size of the gain or loss is greater for running than for up-front trades.25 -7. and vice-versa for a protection seller.55 1. Beyond a point.
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.Lehman Brothers | Quantitative Credit Research
QCR Quarterly. However.65 -5.14 1. the running trade has a higher P&L than the up-front trade.56 -0. we see that buying a bond and buying protection is not a credit-neutral strategy. the longer the issuer survives.
Time (Y) 0 0. the performance of the up-front trade improves relative to running.14
Here we see that the loss due to the spread tightening is greater than the increase in the bond price. and the timing of the credit event has a significant influence on the net P&L of a trade.58 3. Variation in Outcomes: Running versus Upfront Table 7 summarizes the relative performance of running and up-front trades for various scenarios including the ones described above. As the timing of the credit event recedes.00 Running spread 1050 bp 495 bp -$19.69 -1.81
In each case shown the investor has hedged the bond’s face value and so has full principal protection.00 -75. If protection is triggered in one year. the P&L of the up-front trade exceeds that of the running trade. the adverse impact of spread tightening is more pronounced as shown below in Table 6. This means that investors should choose to trade on a running or an up-front basis depending on the strength of their view and their risk preferences. For this reason. as the running spread paid eventually exceeds the initial cost of up-front protection.5277 PV01 Funding ($) 75.
Table 7. the better the performance of an upfront trade relative to running for a protection buyer. We now turn to the formal valuation and marking to market of up-front protection trades and discuss their sensitivity to various market factors. Indeed we see that a trade can switch from being positive value-ondefault to negative value-on-default depending on the timing of a credit event.42 -3. 2003-Q3
up-front CDS. Additionally.00 92. First.
Table 6. Two clear conclusions can be drawn from the various outcomes.4. It shows that a protection buyer would have been better off buying up-front protection on the trade date since this exhibits lower spread sensitivity than a running CDS.00 17.

s+ds] conditional on surviving to time s. the investor has received 200bp over the risk-free rate for assuming no credit risk (we ignore the counterparty risk of the protection seller). See O’Kane and Turnbull (2003) for a discussion. s )λ ( s ) ds  t  
(1)
where λ(s) is the hazard rate. The initial cost of the bond plus protection would be $100. vol. The next step is to calibrate this model in order to value the up-front protection. VALUATION OF UP-FRONT PROTECTION
One starting point for valuing up-front protection is to attempt to use the cash market as a reference. No Credit Event: The investor receives all of the remaining coupons plus par.2. The only difference is that there is uncertainty regarding the timing of the principal payment since this is at the maturity date of the contract or the time of the credit event. Valuation Model The value of the up-front CDS is the expected present value of the contingent payment of (100%–R) made on the face value of the protection following a credit event. suppose that a 5-year bond with a 5% coupon trades at a price of $85 when risk-free rates are 3%.Lehman Brothers | Quantitative Credit Research
QCR Quarterly. 4.
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. suppose the investor was quoted $15 for upfront protection. To determine how much more. T ) = E Q (1 − R ) ∫ Z (t . Q(t. This can be written as:
T   U (t . There are a number of ways to do this. This trade presents an arbitrage as it implies that the investor should pay more than $15 for up-front protection. There are two possible outcomes: Credit Event: The investor receives all the coupons up to the time of the credit event and then receives par (in return for delivering the defaulted asset to the protection seller). s )Q (t .1. There are essentially three ways to do this. Let the current date be time t and consider the problem of pricing an up-front default swap maturing at time T. Z(t. How much should an investor pay for up-front protection? To investigate the economics of the trade. For example. This is simply the value of the protection leg in the standard CDS. This is usually assumed to be deterministic and independent of interest rates. we need a valuation model which can reconcile both the pricing of bonds and up-front CDS.s) is the arbitrage-free survival probability of the reference entity from valuation time t to time s. which we describe next. In both cases. the instantaneous probability of default in the period [s.s) is the Libor discount factor from valuation date t to time s. where we define R as the expected price of the Cheapest To Deliver (CTD) obligation following a credit event. 4. 2003-Q3
4. Calibration of Survival Probabilities Calibration within a risk-neutral framework involves determining the term structure of survival probabilities which refits the market prices of traded assets. The value of up-front protection is then given by the discounted expectation of (100%-R) at the time of the credit event.

The value of the up-front implicitly should be greater to take into account the coupon payments on the bond which would be paid. we use Equation (1) to invert prices and extract survival probabilities. Survival Probabilities from Bond Prices An alternative is to use bond prices. Calibration in these circumstances may be best achieved using some best-fit approach.
5. Survival Probabilities from Up-front Prices The observed price of up-front protection can also be used to extract survival probabilities. Care should be taken to remove default swap basis effects. but it may not be realistic as a distressed credit typically has a downward sloping hazard rate term structure. which should enforce consistent pricing within the CDS market. a flat3 hazard rate. However. Observe that this is greater than par minus the full price of the bond. a 5-year bond trading with a 5% annual coupon and a price of $85 implies a term structure of survival probabilities. and this is shown in the appendix. it implicitly knows about the bond since the survival probabilities have been calibrated to the bond price. the valuation equation (1) of the up-front does not explicitly know about the coupons on the bond. where we noted that an up-front value of $15 presents an arbitrage.
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.1. The question to be answered next is: what is the sensitivity of the up-front protection value to these inputs? 5. we need a valuation formula for bonds which allows us to do so. SENSITIVITY ANALYSIS OF UP-FRONT PROTECTION
The inputs into the valuation of up-front protection are the interest rate term structure. As a result. the CDS spread curve and a recovery rate assumption. In this case. 2003-Q3
Survival Probabilities from CDS Spreads This most straightforward approach. Substituting these results into the up-front pricing formula gives us a value for the up-front protection of $22. The $7 represents the expected present value of the coupon payments on the bond. vol.Lehman Brothers | Quantitative Credit Research
QCR Quarterly. it is also possible that a bootstrapping approach may not be appropriate. a flat 3% risk-free rate.
3 This is the simplest assumption we can make. Sensitivity to Interest Rates The value of up-front protection is the value of (100%-R) paid following a credit event. i. is to bootstrap a term structure of survival probabilities using the term structure of spreads in the CDS market as described in O’Kane and Turnbull (2003). $15 (= $100–15). In this case.3. However. The value of this decreases with increasing interest rates as shown in Figure 2. This is exactly what we expected from our observation in the example at the start of this section. Just to be clear. 4. the investor who buys the bond and buys up-front must pay $85+$22=$107. This assumes the existence of quoted CDS spreads which may not be the case when the credit is trading distressed.e. especially when bonds exist with similar maturities but different coupons and prices. Example Assuming a recovery rate of 40%. This can allow us to price up-front CDS to other maturities.

Maturity
60. we need to determine the sensitivity of the mark-to-market to market factors. Funding Issues
Unlike a running CDS.00
0. vol.
6.T).2.Lehman Brothers | Quantitative Credit Research
QCR Quarterly. However.00
10. Let t be the current valuation date. However this ignores the cost of funding or investing the upfront payment. when evaluating the P&L of a trade.
6.1.T) is the remaining value of protection between t and T. For those trading up-front CDS. then the value of the position is given by:
UF UF M Short ( t . If U(t.
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. which costs nothing to set up.00
S = 1500 bp
50. 2003-Q3
Figure 5. T ) = U( t .
6.
Up-front Price vs.
VALUING AN UP-FRONT POSITION
Valuing an up-front protection trade is different to marking to market a running CDS. the value of an upfront trade is the value of what is paid or received if the contract is unwound minus the value paid for the upfront. Computing the Up-Front Position Value
Consider an investor who has sold protection on an up-front basis at time 0 for T years at a price U(0. T) = − M Long
This is because U(t. For a running CDS trade.00
S = 500 bp
20.00 0 2 4 6 8 10 12 14 16
Years to Maturity
What we have shown so far is the sensitivity of the up-front price to a number of important parameters. The cost of funding (in case of a long protection position) or the value of reinvestment (in case of short protection) must therefore be taken into account.T) is the cost of entering into an offsetting position on the reference credit at time t. The difference is due to the fact that the upfront trade is funded while the running is unfunded. This is addressed in the next section. the P&L of the trade is the MTM of the contract described elsewhere (O’Kane and Turnbull 2003). T ) − U (0.00
30. This may incorporate funding costs for the initial payment of upfront protection. ignoring the coupons paid or received. an upfront CDS involves an initial payment to the protection seller.00
Upfront Price
40.

all the market information from the trade date to maturity is incorporated into a single initial payment U(0. T ) L = [S( t . This will change in value as spreads. the investor’s wealth at time t is given by
U(0.T) with maturity T and which has been offset at valuation time t with a position traded at a spread of S(t. At time 0. T ) L
Clearly. Assuming that this is reinvested at Libor flat. which is contractually fixed at time 0.T) is also done at Libor flat. M RUN ( t . is the present value at time t of a 1bp premium stream which terminates at the earlier of maturity time T or default.T) is given by the value of the protection leg minus the expected present value of the premium leg of the CDS. in an upfront trade the investor has already paid (or received payment) for the remaining protection. This has no sensitivity to any subsequent market inputs and no exposure to future interest rates. t ) − U( t .3. The difference is clear. T) where RPV01(t. For an investor using up-front CDS to buy or sell credit risk. then the net gain or loss from this trade is PLUF ( t . worth U(t. T) = U ( t .Lehman Brothers | Quantitative Credit Research
QCR Quarterly. buying up-front protection for the remaining time from t to T at the price U(t. In an up-front contract. whereas in a running trade part of the payment. In both cases the protection buyer is long the protection which is worth U(t. T) ⋅ B(0. The present value of a running long protection position initially traded at time 0 at a contractual spread of S(0. T) S For a long protection position. Comparison with Running CDS
It is important to compare the value of an up-front CDS contract to the value of the equivalent running CDS contract. this payment is made between t and min[T. If. T) = U(0. In contrast. The difference is in the premium leg. T) − S(0.T). interest rates and recovery rate assumptions change. t ) where B(0. See the references for a discussion of the MTM of running default swaps.t) is the value of a dollar continuously reinvested at Libor between 0 and t. it is essential to understand how sensitive the valuation of the position is to changes in market variables. credit spreads or recovery rates.T). 2003-Q3
Consider the position of an investor selling protection on an up-front basis. vol. T ) ⋅ RPV 01( t . T) = U( t .τ] where τ is the time of the credit event. T )] ⋅ RPV 01( t . T) − S(0. at time t. t ) = −M S ( t .T). assuming that the funding of the initial payment of U(0. the investor enters into an offsetting contract.T). the investor receives U(0.T). the spread leg of the standard CDS is sensitive to all of these market variables since it is the discounted expectation of risky spread payments. T)B(0.
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. T) ⋅ B(0. different borrowing and lending rates can break this symmetry. In other words.
6. T) − U (0. we have
UF PLUF ( t . We now examine the sensitivity of running and upfront trades to spreads and interest rates.T).

T) − S(0.T) while that of the running CDS tends to (1-R) since the value of the premium leg tends to zero. the MTM becomes positive. There is a fundamental difference between running and up-front which is that in a running CDS both legs of the contract trade have an interest rate sensitivity. However.5.00 20.00 60. Interest Rate Sensitivity
Figure 9 compares the interest rate sensitivity of MTM for up-front and running CDS as spreads change. the value of the MTM is negative. T) = [S( t .00 -40. the MTM of a long protection position is given by M RUN ( t .T)=S(0. the slope of the running CDS curve is different to that of the up-front CDS because the running CDS has a risky PV01 effect – at low spreads the risky PV01 is high. However. since the implied default probability increases and so the value of the protection increases.00 0.
6.4.
Figure 8. the risky PV01 decreases.
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. since both the premium and the protection legs are sensitive to spread changes. As the spread increases beyond S(t. Recall. Relative Spread Sensitivity of the MTM of Up-front and Running CDS.T).00 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Upfront
Spread
We see the same sort of behavior for the up-front protection. This makes the running protection more negative at lower spreads and more positive at high spreads. Sensitivity to Spreads
Both the MTM of an up-front and running long protection CDS increase as spreads widen. At very high spreads the upfront CDS value tends asymptotically to (1-R)-U(0.
80. while for high spreads the risky PV01 is low. 2003-Q3
6. a running CDS is more sensitive to spread changes than an up-front CDS. vol.00 -20. T)] ⋅ RPV 01( t .T) increases. This is shown in Figure 8. T ) L As low market spreads.00 -60.00
Running
MTM (Long Protection)
40.Lehman Brothers | Quantitative Credit Research
QCR Quarterly. As the value of S(t. The MTM of a running CDS is dependent on two opposing factors. The IR01 is defined as the change in the value for a long protection position for a 1bp parallel change in the Libor curve.

but wishes to hedge downside risk “just in case”. vol. For protection buyers.
Interest Rate Sensitivity of MTM for Running and Up-front Trades
0. and an investor’s P&L can be significantly different depending on whether protection is bought on an up-front or running basis. For protection sellers.02 0.01 -0.
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10000
.
• Buying a bond and buying protection is not a credit-neutral trade. The net P&L depends on the timing of the credit event.00 -0. The interest rate sensitivity of the MTM of the up-front CDS is only to the contingent incoming payment of (100%-R) and so is negative. an up-front trade will outperform a running trade. and also take exposure to a different risk profile than running trades. CONCLUSIONS
Up-front CDS trades are common for short-dated and distressed bonds. The relative performance of running and up-front trades depends on whether a credit event occurs and when. This is in order to avoid locking in a high contractual spread for the life of the trade. If the issuer survives.02 0
Running
Upfront
1000
2000
3000
4000
5000
6000
7000
8000
9000
Spread
At low spreads the MTM of the running CDS is negative so that an increase in interest rates increases the value of the contract and the IR01 is positive. For the same reason. • Protection buyers who have a view that default is almost certain should prefer to trade on a running CDS format since the spread will only be paid until the credit event.
Up-front trades can therefore be used to express a view on the timing of a credit event. • A protection buyer who expects the reference credit to survive. protection sellers who view default as imminent should prefer to trade on an up-front basis. However. they offer the opportunity for better carry trades and a way to avoid being locked into paying high spreads.
7. they are attractive as a means to lock in the PV of protection as a sure payment rather than a risky cashflow stream.Lehman Brothers | Quantitative Credit Research
QCR Quarterly. at very high spreads the sensitivity to interest rates of both contract types tends to zero as they both tend to contracts paying a certain 1R immediately. • A protection buyer who is taking a strong view on a spread movement should prefer a running CDS as this exhibits a higher spread sensitivity than an upfront CDS.01 -0.01
IR01 (Long Protection)
0. We summarise the main conclusions below. should prefer to pay for protection in up-front form rather than as a running spread. Equally the downside can be greater. Which is chosen should reflect the investor’s view.01 0. 2003-Q3
Figure 9.

Jarrow and Turnbull (1995). t m )) 2 j=1 m =1
The first term is the sum of the risky discounted coupons. If coupons are paid semi-annually. O’Kane and McAdie (2001). weighted by the probability that the issuer survives to maturity. Suppose the full price at time t of a bond issued by the same issuer as the reference credit.T). Vol 50 (1995). Mashal and Wang (2003) for details of a fitting approach. 53-85. Lehman Brothers. the model-based valuation formula for a bond is given by
B( t. vol. T) + R ∑ Z(t. t j ) +Z(t. We have assumed the issuer defaults at M discrete times and that coupons default with no recovery.
8. cross default provisions mean that they should default together and so have the same term structure of survival probabilities Q. August 2003. t j )Q(t. March 2001. Modelling Credit: Theory and Practice. is given by B(t. T)Q(t. Estimation of Implied Default and Survival Probabilities from Credit Bond Prices. Journal of Finance. O’Kane and Schloegl (2001). The survival probabilities can now be calibrated to a term structure of bond prices using some best-fit technique. The second term is the PV of the principal repaid at maturity. maturing in T years and paying an annual coupon rate of C. The third term is the PV of the price of the bond after a credit event. T ) =
M C n ∑ Z( t. February 2001. Pricing Derivatives on Financial Securities Subject to Credit Risk. 2003-Q3
REFERENCES
Berd. R. APPENDIX
Given that a bond and a credit default swap are linked to the same reference entity. Lehman Brothers QCRQ.
August 2003
15
. See Berd. Trading the Basis. Risk Magazine. which is realised if the credit event occurs before maturity. t m −1 ) − Q(t.Lehman Brothers | Quantitative Credit Research
QCR Quarterly. October 2001. Mashal and Wang (2003). t m )(Q(t. O’Kane (2001) Credit Derivatives Explained.

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